Port-Hamiltonian system model identification of a micro-channel ?

In this paper we identify the parameters for a finite Port-Hamiltonian system (PHS) model of a micro-channel using ordinary least squares method. The PHS model is based on the interconnection of basic finite elements equivalent to capacitors, inductance and resistors. The interconnection of several basic element models can represent the micro-channel model behavior. The parameter capacitance depends on the geometry of the channel, but the inertance, the uncontrolled and the controlled resistance are difficult to measure. The PHS based Fluidstructure interconnected system can estimate the behavior of the process as well as Partial Differential Equations (PDE) based models. The resultant model can then be used to design a controller to have a desired level at any given position in the micro-channel.